Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}9x-5y &= -8 \\ 4x-5y &= 2\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $-5y = -4x+2$ Divide both sides by $-5$ to isolate $y$ $y = {\dfrac{4}{5}x - \dfrac{2}{5}}$ Substitute this expression for $y$ in the first equation. $9x-5({\dfrac{4}{5}x - \dfrac{2}{5}}) = -8$ $9x - 4x + 2 = -8$ Simplify by combining terms, then solve for $x$ $5x + 2 = -8$ $5x = -10$ $x = -2$ Substitute $-2$ for $x$ back into the top equation. $9( -2)-5y = -8$ $-18-5y = -8$ $-5y = 10$ $y = -2$ The solution is $\enspace x = -2, \enspace y = -2$.